In solving the system of equations, [A] {x} = {b} [5 2 1 3] (x_1 x_2) = (5 2) if

Question

In solving the system of equations, [A] {x} = {b} [5 2 1 3] (x_1 x_2) = (5 2) if the inverse of the coefficient matrix is A^-1 = [0.231 -0.154 -0.077 0.385] The conditioning number of the matrix [A] using the L_infinity norm is (a) not computable because A^-1 has negative entries. (b) K(A) = 3.231, the system is well conditioned, and small residuals mean an accurate solution has been obtained. (c) K(A) = 3.231, the system is ill-conditioned, and small residuals mean an accurate solution has been obtained. (d) K(A) = 591, 267.25, the system is ill-conditioned and small residuals do not mean accurate solution has been obtained. (e) none of the above

Explanation / Answer

condition number of matrix

||A|| ||A-1||

||A|| = max ((5+1) ,(2+3)_

=max(6,5) = 6

||A-1|| = max((0.231 +0.077),(0.154 + 0.385))

=0.539

hence

condition number = 6*0.539 = 3.234

If the condition number is very large, then the matrix is said to be ill-conditioned.

option B) is correct

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